Consider the polynomial `f(x)=a x^2+b x+cdot` If `f(0)=0,f(2)=2,` then the minimum value of `int_0^2|f^(prime)(x)|dxi s___`

Consider the polynomial f(x)=a x^2+b x+cdot If f(0),f(2)=2, then the minimum value of int_0^2|f^(prime)(x)dxi s___

If f(0)=1,f(2)=3,f^'(2)=5 ,then find the value of int_0^1xf^('')(2x)dx

If f continuous and differentiable on [0,1] with f(0) = 0 and f(1)=1, then the minimum value of int_0^1(f^(prime)(x))^2dx is

If f''(x) = sec^(2) x and f (0) = f '(0) = 0 then:

Suppose f is continuous on [a,b] & f(a)=f(b)=0 & int_(a)^(b)f^(2)(x)dx=1 then the minimum value of int_(a)^(0)(f^(')(x))^(2)dx int_(a)^(b) x^(2)f^(2)(x)dx is k , then 8k is

If f(x) is continuous and int_(0)^(9)f(x)dx=4 , then the value of the integral int_(0)^(3)x.f(x^(2))dx is

Let f(x) be a differentiable function in the interval (0, 2) then the value of int_(0)^(2)f(x)dx

If f(0)=2,f'(x)=f(x),phi(x)=x+f(x)" then "int_(0)^(1)f(x)phi(x)dx is

If int_(0)^(x^(2)(1+x))f(t)dt=x , then the value of f(2) is.

Let f(x0 be a non-constant thrice differentiable function defined on (-oo,oo) such that f(x)=f(6-x)a n df^(prime)(0)=0=f^(prime)(x)^2=f(5)dot If n is the minimum number of roots of (f^(prime)(x)^2+f^(prime)(x)f^(x)=0 in the interval [0,6], then the value of n/2 is___